Question

Derive the equation of the parabola with a focus at (−5, −5) and a directrix of y = 7

Answer 1

have you covered parabolas yet?

Answer 2

Insert the points (-5 ,-5) and (x , 7) into this formula

\((x - x_1)^2+ (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2\)
\((x + 5)^2 + (y + 5)^2 = (y - 7)^2\)

Now Expand:
\(x^2 + 10x + 25 + y^2 + 10y + 25 = y^2 -14y + 49\)

\((x + 5)^2 -24 = -10y - 14y\)

\((x + 5)^2 - 24 = -24y\)

\(-\dfrac{(x + 5)^2 - 24}{24} = y\)

\(y = -\dfrac{(x + 5)^2}{24} + 1\)

Answer 3

oh ok @Hero